An Improved Lower Bound for $g^{(4)}(18)$

Abstract

The cardinality of the minimal pairwise balanced designs on $v$ elements with largest block size $k$ is denoted by $g^{(k)}(v)$. It is known that $30\le g^{(4)}(18)\le 33.$In this note, we show that $31\le g^{(4)}(18).$